# Computer Age Statistical Inference: Algorithms, Evidence, by Bradley Efron

By Bradley Efron

The twenty-first century has obvious a wide ranging enlargement of statistical technique, either in scope and in impression. 'Big data', 'data science', and 'machine studying' became general phrases within the information, as statistical tools are delivered to endure upon the big information units of recent technology and trade. How did we get right here? And the place are we going? This e-book takes us on an exciting trip during the revolution in facts research following the creation of digital computation within the Fifties. starting with classical inferential theories - Bayesian, frequentist, Fisherian - person chapters soak up a sequence of influential themes: survival research, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after version choice, and dozens extra. The fairly glossy procedure integrates method and algorithms with statistical inference. The publication ends with hypothesis at the destiny course of information and knowledge technology.

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**Example text**

The ﬂat prior, g. / constant, results in the dangerous overestimate O 610 D x610 D 5:29. A more appropriate uninformative prior appears as part of the empirical Bayes calculations of Chapter 15 (and gives O 610 D 4:11). The operative point here is that there is a price to be paid for the desirable properties of Bayesian inference. Attention shifts from choosing a good frequentist procedure to choosing an appropriate prior distribution. This can be a formidable task in high-dimensional problems, the very kinds featured in computer-age inference.

X/; Â 2 3 ; x 2 Xg; The multiparameter case is considered in the next chapter. 13) 42 Fisherian Inference and MLE where is an interval of the real line, possibly inﬁnite, while the sample space X may be multidimensional. 2) in the one-dimensional case. 15) where we are assuming the regularity conditions necessary for differentiating under the integral sign at the third step. Â / has mean 0 and variance IÂ . The term “information” is well chosen. 18) and that no “nearly unbiased” estimator of Â can do better.

This is not a comforting criterion for the statistician’s clients, who are interested in their own situations, not everyone else’s. Here we are only assuming hypothetical repetitions of the speciﬁc problem at hand. 18 Frequentist Inference What might be called the strong deﬁnition of frequentism insists on exact frequentist correctness under experimental repetitions. Pivotality, unfortunately, is unavailable in most statistical situations. Our looser deﬁnition of frequentism, supplemented by devices such as those above,7 presents a more realistic picture of actual frequentist practice.